I am also having this problem in a CFA that I am running. It seemed that this issue happened with the same model that I've run in Mplus versions 5.1, 6.0, and 6.1, in which some loadings are non-significant in the unstandardized results, but are significant (or marginal) in the fully standardized (STDYX) results.

Please let me know if you'd also like me to send the output and license number to support. Thank you in advance!

Thanks for your reply Linda! I'm writing up the results of the CFA for publication. Do you have a suggestion for which results to use for reporting as well as to draw the figure for the CFA (i.e., the correlations between the factors and the loadings are not always consistent between the two results)?

Linda, I just want to make sure that the raw and standardized results should vary so much. For example, on the loadings I have p-values that are .12 vs. .001 (raw vs. stdyx) and on the correlations between the factors I have p-values that are .18 vs. .002 and .04 vs. .11 (raw vs. stdyx). So, from these examples you can see that the difference is often extreme, and often the stdyx result is significant, but not always. I just want to double check that it is not strange for the results to be this different, and also if you can give some explanation or resource for why this difference occurs.

I really can't say much without seeing the outputs where you see the differences. Otherwise I am just guessing. You can send them to support along with your license number if you want. The two coefficients have different sampling distributions.